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Quartic Regression Calculator — result sheet
Fit a fourth-degree least-squares polynomial to paired data and evaluate it at a target value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Choose a₀…a₄ to minimize Σ[yᵢ−(a₀+a₁xᵢ+a₂xᵢ²+a₃xᵢ³+a₄xᵢ⁴)]²; R²=1−SSE/SST.
The quartic coefficients are solved from the least-squares normal equations, then the fitted polynomial is evaluated at the requested target.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Comma-separated numeric values.
- Y values — Comma-separated numeric values matching X.
- Target x — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| X values | -2, -1, 0, 1, 2, 3 |
| Y values | 16, 1, 0, 1, 16, 81 |
| Target x | 4 |
Fit is approximately y=x⁴; predicted y at x=4 is 256; R² = 1.
Assumptions and limits
- X and Y contain equal-length finite lists with at least five independent design points.
- Least squares is sensitive to outliers and high-degree fits can behave poorly outside the observed range.
- R² describes in-sample fit and is not a guarantee of causal structure or predictive performance.
- The calculation does not provide coefficient uncertainty intervals.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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